Aqueous Homogeneous Reactors (AHR) are used for the production of medical isotopes and are characterized by high economy and safety. Due to the closely packed multiple cooling coils in the core, the thermal–hydraulic analysis of AHR is grid-heavy and computationally time-consuming. Firstly, in order to reduce computational consumption, a coarse-mesh method is employed to model the core and cooling coil based on GeN-Foam. For the core, a Eulerian-Eulerian two-phase flow model with implanted fission gas mass source term and fission deposition energy source term is used. For the cooling coil, solution matrices for tube wall and cooling water are developed and constructed based on the finite volume method. Secondly, in order to improve the computation speed, the parallel computation of cooling coils is developed with GeN-Foam parallel framework. Thirdly, the developed code was applied to carry out a 3D thermal–hydraulic analysis of the MIPR core. The results show that the code is able to calculate the fission gas and energy deposition, and the core has reasonable temperature and void fraction distribution; the code is able to correctly identify and build the virtual mesh of the cooling coil, and the trends of the tube wall and cooling water temperature changes are consistent with the physical processes. Moreover, the speed of computation can be significantly increased by optimizing numerical algorithms and parallel strategies. This study can provide a reference for the three-dimensional thermal–hydraulic calculation of AHR.